The sum of two numbers is $51$, and their difference is $21$. What are the two numbers?
Explanation: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 51}$ ${x-y = 21}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 72 $ $ x = \dfrac{72}{2} $ ${x = 36}$ Now that you know ${x = 36}$ , plug it back into $ {x+y = 51}$ to find $y$ ${(36)}{ + y = 51}$ ${y = 15}$ You can also plug ${x = 36}$ into $ {x-y = 21}$ and get the same answer for $y$ ${(36)}{ - y = 21}$ ${y = 15}$ Therefore, the larger number is $36$, and the smaller number is $15$.